If I use the MX snapshot tool to create an .iso file of my installation that I have configured
exactly like I want it and I want to use that .iso to create a live USB to install MX on another
person's computer so that the installation is exactly like mine, there appears to be is no provision
in the installation to use a different username.

I don't want to select the new user snapshot option when creating the .iso file because then I would have
to do all the configuration again (setting up the desktop, configuring the browser, etc.).

So, my question is, can I change the original installation username after the installation,
or will that completely screw up the system ?

If it is possible, is the following the correct command to do so ?

usermod -l login-name old-name (where login-name would be the new username and old-name the current one)

And if that will work, do I need to do anything else ?

For example, will that command also change the previous username folder under the home folder
to the new username or will I have to do that as well ?

So, my question is, can I change the original installation username after the installation,
or will that completely screw up the system ?

If it is possible, is the following the correct command to do so ?

usermod -l login-name old-name (where login-name would be the new username and old-name the current one)

And if that will work, do I need to do anything else ?

For example, will that command also change the previous username folder under the home folder
to the new username or will I have to do that as well ?

Such an option is not realy provided. Esp. after the fact. You coul do somethin in preparation.
But afterwards, lot#s of changes, e.g with the settings e.g.

man usermod | grep -A3 -- --login
-l, --login NEW_LOGIN
The name of the user will be changed from LOGIN to NEW_LOGIN. Nothing else
is changed. In particular, the user's home directory or mail spool should
probably be renamed manually to reflect the new login name.

You might try create a new user, copy over with MX-user the whole home from demo to that new user,
and see how far you can go with that new user.
I know, that's a bit missing, to provide a bullet prove rename my user, so evrything will work afterwards.
...

as fehlix said, there will be lots of changes. at a minimum, you'll need to rename the home folder I think. and if you've got things in the home folder that use specific paths (conky, bluetooth) you might need to change some file paths as well. that might also include some of the Xfce configuration files, depending on what kind of customizations you've done.

when I do snapshots for other people to use, I sync back any changed config files in the home folder back to /etc/skel/.config. files in that directory become the basis for new user home folders, and you'll find the mx defaults in there. If you do that, then you can use the non-personal snapshot version and the installer will present the normal user creation screen at the end of the install.